Poromechanics of freezing materials

When subjected to a uniform cooling below the freezing point a water-infiltrated porous material undergoes a cryo-deformation resulting from various combined actions: (i) the difference of density between the liquid water and the ice crystal, which results in the initial build-up of an in-pore pressure at the onset of crystallization; (ii) the interfacial effects arising between the different constituents, which eventually govern the crystallization process in connection with the pore access radius distribution; (iii) the drainage of the liquid water expelled from the freezing sites towards the air voids; (iv) the cryo-suction process, which drives liquid water towards the already frozen pores as the temperature further decreases; (v) the thermomechanical coupling between the solid matrix, the liquid water and the ice crystal. We work out a comprehensive theory able to encompass this whole set of actions. A macroscopic approach first provides the constitutive equations of freezing poroelastic materials, including the interfacial energy effects. This approach reveals the existence of a thermodynamic state function—namely the liquid saturation degree as a function of the temperature only. The macroscopic ice-dependent poroelastic properties are then upscaled from the knowledge of the elastic properties of the solid matrix, of the pore access radius distribution, and of the capillary curve. The theory is finally illustrated by analysing quantitatively the effects of the cooling rate and of the pore radius distribution upon the cryo-deformation of water-infiltrated porous materials. The theory succeeds in accounting for the experimentally observed shrinkage of embedded air voids, while predicting the partial melting of the ice already formed when the cooling suddenly stops.     

On the Deformation of Functionally Graded Porous Elastic Cylinders

This paper is concerned with the linear theory of inhomogeneous and orthotropic elastic materials with voids. We study the problem of extension and bending of right cylinders when the constitutive coefficients are independent of the axial coordinate. First, the plane strain problem for inhomogeneous and orthotropic elastic materials with voids is investigated. Then, the solution of the problem of extension and bending is expressed in terms of solutions of three plane strain problems. The results are used to study the extension of a circular cylinder with a special kind of inhomogeneity. The influence of the material inhomogeneity on the axial strain is established.      

Mechanical modelling of ductile fracture

Mechanical models of material failure by void growth to coalescence are described to give a brief overview of methods applied in the analysis of ductile fracture. Approximate constitutive relations for porous ductile materials are discussed, modelling both the nucleation and growth of voids. The application of the material models is illustrated by numerical analyses for a tensile test specimen and for dynamic, ductile crack growth. Unstable void growth is a relevant mechanism in ductile materials subject to a high level of triaxial tension. The analysis of such cavitation instabilities in elastic-perfectly plastic materials is discussed for axisymmetric stress states, and the relevance to metal/ceramic components is emphasized.General Lecture presented at the 10th Italian National Congress of Theoretical and Applied Mechanics; AIMETA, Pisa, October 1990.     

多孔Mooney-Rivlin材料矩形板的单向拉伸

本文利用不同可压超弹性材料大变形的Mooney-Rivlin应变能函数研究了含有多个微孔的矩形板在单向拉伸作用下的有限变形和受力分析。首先利用不可压条件得到了文中所给的含有某种对称性分布的多个微孔的矩形板的变形模式函数，其中所含的一个参数可由远离微孔的无穷远处的变形状态确定，另一个参可用最小势能原理导出变分近似解。文中详细分析了板中微孔（一个，三个和五个）随载荷作用的增长情况和微孔边缘应力的分布情况，并进行了比较。讨论了微孔的个数和排列方式，微孔的孔间距离等因素对微孔增长和应力分布的影响。     

Dimensionality effects in void-induced explosive sensitivity

The dimensionality of defects in high explosives controls their heat generation and the expansion of deflagrations from them. We compare the behaviour of spherical voids in three dimensions to that of circular voids in two dimensions. The behaviour is qualitatively similar, but the additional focusing along the extra transverse dimension significantly reduces the piston velocity needed to initiate reactions. However, the reactions do not grow as well in three dimensions, so detonations require larger piston velocities. Pressure exponents are seen to be similar to those for the two-dimensional system.     

Experimental Cosserat elasticity in open-cell polymer foam

Reticulated open-cell polymer foams exhibit substantial size effects in torsion and bending: slender specimens are more rigid than anticipated via classical elasticity. Such size effects are predicted by Cosserat (micropolar) elasticity, which allows points to rotate as well as translate and incorporates distributed moments (couple stresses). The Cosserat characteristic length is larger than the cell size. The Cosserat coupling coefficient is larger than in dense closed-cell foams and approaches 1 for foam with 0.4 mm cells.     

设计脆性材料的冲击塑性

通过微结构设计提升脆性功能材料的冲击塑性, 将有助于避免或延缓失效的发生. 提出在脆性材料中植入特定的微小孔洞以改善其冲击塑性的设计方法. 采用一种能够定量表现脆性材料力学性质的格点-弹簧模型, 研究了孔洞排布方式对脆性材料冲击响应的影响. 孔洞随机排布的多孔脆性材料具有明显高于致密脆性材料的冲击塑性, 而设计规则的孔洞排布方式将有助于进一步提升脆性材料的冲击塑性. 对150 m/s活塞冲击下气孔率5%的多孔样品的介观变形特征分析表明, 孔洞规则排布的样品中孔洞贯通和体积收缩变形占主导, 而孔洞随机排布的样品中剪切裂纹长距离扩展和滑移与转动变形占主导. 尽管在宏观的Hugoniot应力-应变曲线上, 两种孔洞排布方式的样品都表现出三段式响应特征(线弹性阶段、塌缩变形阶段和滑移与转动变形阶段), 但孔洞规则排布时孔洞塌缩变形阶段对整体冲击塑性的贡献更大. 研究揭示的规则排布孔洞增强脆性材料冲击塑性的原理, 将有助于脆性材料冲击诱导功能失效的预防.     

Elastic–plastic ductile damage model based on strain-rate plastic potential

Modeling of ductile damage is generally done using analytical potentials, which are expressed in the stress space. In this paper, for the first time it is shown that strain-rate potentials which are exact conjugate of the stress-based potentials can be instead used to model the dilatational response of porous polycrystals. A new integration algorithm is also developed. It is to be noted that a strain-rate based formulation is most appropriate when the plastic flow of the matrix is described by a criterion that involves dependence on all stress invariants. In such cases, although a strain-rate potential is known, the stress-based potential cannot be obtained explicitly. While the proposed framework based on strain-rate potentials is general, for comparison purposes in this work we present an illustration of the approach for the case of a porous solid with von Mises matrix containing randomly distributed spherical cavities. Comparison between simulations using the strain-rate based approach and the classical stress-based Gurson's criterion in uniaxial tension is presented. These results show that the model based on a strain-rate potential predicts the dilatational response with the same level of accuracy.     

Measurements of hall-effect and sheet resistivity as a function of temperature on hot,phosphorous implants in silicon

Abstract

Results of Hall-effect measurements as a function of temperature on a layer formed by hot, phosphorous (P³¹) implant in Si at 400 keV energy in a random direction are presented; the dose used was 10¹⁵ ions cm^?2. The electrical behaviour of the layer as a function of isochronal annealing was examined.

A detailed analysis of the measured quantities n _8eff, the effective surface density of free carriers, and μ_eff, the effective mobility, down to 4.2°K is presented using the integral equations:

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These formulae were solved numerically, the input data viz: the distribution of donor centres and compensating damage centres being assumed from the current literature.

Results from this analysis indicate a rather complicated distribution of current flow in the layer as a function of temperature, indicating that the traditional interpretation of Hall measurements based on a homogeneous distribution model is of questionable validity.